Validation of the CMS Magnetic Field Map

The Compact Muon Solenoid (CMS) is a general purpose detector, designed to run at the highest luminosity at the CERN Large Hadron Collider (LHC). Its distinctive features include a 4 T superconducting solenoid with 6-m-diameter by 12.5-m-length free bore, enclosed inside a 10,000-ton return yoke made of construction steel. The return yoke consists of five dodecagonal three-layered barrel wheels and four end-cap disks at each end comprised of steel blocks up to 620 mm thick, which serve as the absorber plates of the muon detection system. To measure the field in and around the steel, a system of 22 flux loops and 82 3-D Hall sensors is installed on the return yoke blocks. A TOSCA 3-D model of the CMS magnet is developed to describe the magnetic field everywhere outside the tracking volume measured with the field-mapping machine. The magnetic field description is compared with the measurements and discussed.


Introduction
The muon system of the Compact Muon Solenoid (CMS) detector includes a 10,000-ton yoke comprised of the construction steel plates up to 620 mm thick, which return the flux of the 4 T superconducting solenoid and serve as the absorber plates of the muon detection system [1][2][3][4]. During the LHC long shutdown occurring in 2013/2014 the CMS magnet yoke is upgrading with the additional 14-m-diameter end-cap disks at the extremes of the muon detection system [5]. The presence of the 0.125-m-thick disks changes the magnetic flux 2 density distribution in the adjacent end-cap disks by 25% in average. This requires developing the new magnetic field map to be used in the detector simulation and the event reconstruction software.
The magnetic flux density in the central part of the CMS detector, where the tracker and electromagnetic calorimeter are located, was measured with precision of 7·10 -4 with the field-mapping machine at five central field values of 2, 3, 3.5, 3.8, and 4 T [6]. To describe the magnetic flux everywhere outside the measured volume, a three-dimensional (3-D) magnetic field model of the CMS magnet has been developed [7] and calculated with TOSCA [8] when the detector began operation. The model reproduces the magnetic flux density distribution measured inside the CMS coil with the field-mapping machine within 0.1% [9]. The modification of this model for the upgraded CMS magnet yoke requires validating the model by comparing the calculated magnetic flux density with the measured one at least in selected regions of the CMS magnetic system.
A direct measurement of the magnetic flux density in the yoke-selected regions was provided during the CMS magnet test of 2006 with 22 flux loops of 315÷450 turns wound around the yoke blocks. The "fast" (190 s time-constant) discharges of the CMS coil made possible by the protection system, which is provided to protect the magnet in the event of major faults [10,11], induced in the flux loops the voltages caused by the magnetic flux changes. An integration technique [12,13] was developed to reconstruct the average initial magnetic flux density in steel blocks at the full magnet excitation, and the contribution of the eddy currents was calculated with ELECTRA [14] and estimated on the level of a few per cent [15].
The results of the magnetic flux measurements done with the flux loops and comparison the obtained values with the calculations performed with the previous TOSCA CMS magnet model are described elsewhere [16].
In present paper we compare the calculations done with the recent CMS magnet model with the measurements performed with the flux loops in the yoke steel and with the 3-D Hall probes installed at the steel-air interfaces in the gaps between the CMS yoke parts. These comparisons allow validating the magnetic field maps to be used for the upgraded CMS detector. 3

The CMS Magnet Model Description
The CMS magnet model for the upgraded detector is presented in Fig. 1   The dimensions of the yoke parts and the superconducting coil modules are described elsewhere [16]. The operational current of the CMS superconducting coil is 18.164 kA.

Steel Magnetic Properties Description
Three different B-H curves of the construction steel of the CMS magnet yoke are used in the model. The first curve describes the magnetic properties of the barrel wheel thick plates in the second and third layers. Second curve describes the magnetic properties of thin plates around the thick plates of the second and third barrel wheel layers, and also the properties of the plates of the first layers and the tail catcher plates of the barrel wheels. This curve is used as well for the extensions of the forth end-cap disks, the forward hadronic calorimeter absorbers and shields, and steel collars and rotating shields around the beam pipe. Finally, the third curve describes the magnetic properties of the nose and end-cap disks, the cart plates, keels, and the steel floor. 5

Magnetic Flux Density
The measurements used for the comparisons were obtained in the CMS magnet test during two current cycles on August 17 and 28, 2006 shown in Fig. 3.   19.14 kA. In addition to these comparisons the model perfectly describes the magnetic flux density distribution inside the CMS coil within 0.1% in accordance with the previous model consisted of two separate halves of the yoke [9], [16].

Conclusions
The new CMS magnet model is developed to prepare the magnetic field maps for the upgraded CMS detector. The model is validated by the comparison of the calculated magnetic flux density with the measurements done in the CMS magnet selected regions with the flux loops and 3-D Hall sensors.